# Tag Info

## Hot answers tagged laplacian

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### Help with a PDE

Set $q(x, y) = p(x, y)+B$. Then,  Δ q = \frac{\partial^2 q(x, y)}{\partial x^2}+\frac{\partial^2 q(x, y)}{\partial y^2} = \frac{\partial^2 p(x, y)}{\partial x^2}+\frac{\partial^2 p(x, y)}{\partial y^...
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### Find that of $\frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2}$ equals $= \frac{\partial^2 f}{\partial u^2} + ...$

The keyword here is "chain of rule". Consider a function $z=f(u,v)$ such that $\frac{\partial f}{\partial u}$ and $\frac{\partial f}{\partial v}$ there exists and $u=g(x,y)$ and $v=h(x,y)$ ...
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### How can I solve Laplace Tranformation of $1/s^{5/2}$?

Using TravorLZH's idea we have for $x>-1$, \begin{align*} \mathcal{L}\{t^x\}&=\int_0^\infty t^xe^{-st}dt,\quad\text{doing }u=st\\ &=\int_0^\infty \left(\frac{u}{s}\right)^xe^{-u}\frac{du}{s}...
• 1,490

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